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Results tagged with algebraic-groups
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user 51424
Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
13
votes
0
answers
701
views
Uniform proof of Hasse principle for algebraic groups?
Let $G$ be a simply connected semi-simple linear algebraic group over a global field $k$. The Hasse principle for algebraic groups states that the map $$H^1(k,G)\rightarrow\prod_vH^1(k_v,G)$$ is injec …
- 5,958
8
votes
Accepted
Ideal of the boundary of $G/U \subset \overline{G/U}$
Here is one way to see it, via classifying $G$-invariant radical ideals. (This has the bonus that it implicitly describes the boundary.)
Lemma: $G$-invariant ideals $I$ of $\mathbb{C}[G/U]$ are in bij …
- 5,958
3
votes
Accepted
Subgroup of $\mathrm{GL}_n$ stabilizing linear subspace skew-symmetric matrices
Here is the worst possible proof of all but one case, namely $m=r=3$ (but this is not included in your question as stated, though I think it is claimed in the paper.)
Let $r$ denote the dimension of …
- 5,958
8
votes
How should I think about the Grothendieck-Springer alteration?
The answer to 1) is that this is a special case of a broader phenomenon for symplectic resolutions (though I think some features are specific to the Grothendieck-Springer case.) For instance you have …
- 5,958